1. Field of the Invention
The present invention relates generally to a quadrature amplitude modulation/phase shift keying (QAM/PSK) receiver, and more particularly, to a carrier restoration apparatus and method that compensates for a frequency offset and a phase jitter of a carrier.
2. Background of the Related Art
Typically, a quadrature amplitude modulation (QAM) is used for cable transmission/reception of compressed digital video data in a HDTV. Especially, the 256 QAM modulation is performed in a manner that the compressed video data is encoded for transmission to output 256 constellations corresponding to 8 bits per symbol period (i.e., 5.3607 MHz) as vector values, orthogonal projected values of the vector values on orthogonal axes I and Q are carrier-suppression-modulated by sine and cosine waves, respectively, and then the modulated waves are added together to be transmitted.
In order for a receiving end to obtain the vector values of the 256 constellations again by demodulation, it is required to restore the carrier that is phase-synchronized with the carrier of the received signal and has not been modulated. That is because the orthogonal projection values of the vector values of the 256 constellations on the orthogonal axes I and Q can be obtained by multiplying the received signal by the sine and cosine waves phase-synchronized with the carrier of the received signal, respectively.
Specifically, a carrier restoration section mounted on the QAM receiver in the HDTV cable transmission system should rapidly acquire and track a frequency offset Δω of several hundred KHz and a residual phase jitter Δθ generated from a tuner or RF oscillator to minimize them. Also, the carrier restoration section should perform a high-reliability acquisition/tracking operation even under a low signal-to-noise ratio (SNR) and a severe channel ISI (i.e., ghost).
FIG. 1 is a block diagram illustrating the construction of a general television (TV) receiver. According to this TV receiver, a preprocessing section 11 outputs to a carrier restoration section 12 a pass-band digital signal having a frequency offset and phase jitter. The carrier restoration section 12 modulates the pass-band digital signal outputted from the preprocessing section 11 into sine/cosine waves to generate a base-band digital signal from which the frequency offset and the phase jitter are removed. The base-band digital signal is outputted to a post-processing section 13.
For example, if it is assumed that the carrier restoration section of FIG. 1 restores the carrier of the signal modulated by the QAM, the effect exerted by a phase error at that time is as follows.
That is, if it is defined that I(t) and Q(t) are inphase and quadrature base-band signals, and a modulated signal is fc, a QAM-modulated signal S(t) is expressed by the following equation 1.S(t)=I(t)*cos(2πfct)−Q(t)*sin(2πfct)  [Equation 1]
If the modulated signal is then demodulated into two inphase and quadrature carrier waves having a phase error φ, the base-band signals as shown in the following equations 2 and 3 are obtained.                                                                         DI                ⁡                                  (                  t                  )                                            =                            ⁢                              LPF                ⁢                                  {                                                            S                      ⁡                                              (                        t                        )                                                              *                                          cos                      ⁡                                              (                                                                              2                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                              c                                                        ⁢                            t                                                    +                          ϕ                                                )                                                                              }                                                                                                        =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                      I                    ⁡                                          (                      t                      )                                                        *                                      cos                    ⁡                                          (                      ϕ                      )                                                                      -                                                      (                                          1                      /                      2                                        )                                    *                                      Q                    ⁡                                          (                      t                      )                                                        *                                      sin                    ⁡                                          (                      ϕ                      )                                                                                                                              [                  Equation          ⁢                                          ⁢          2                ]                                                                                    DQ                ⁡                                  (                  t                  )                                            =                            ⁢                              LPF                ⁢                                  {                                                            S                      ⁡                                              (                        t                        )                                                              *                                          sin                      ⁡                                              (                                                                              2                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                              c                                                        ⁢                            t                                                    +                          ϕ                                                )                                                                              }                                                                                                        =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                      I                    ⁡                                          (                      t                      )                                                        *                                      sin                    ⁡                                          (                      ϕ                      )                                                                      -                                                      (                                          1                      /                      2                                        )                                    *                                      Q                    ⁡                                          (                      t                      )                                                        *                                      cos                    ⁡                                          (                      ϕ                      )                                                                                                                              [                  Equation          ⁢                                          ⁢          3                ]            
cos(φ) of the first term of Equation 2 and of the second term of Equation 3 represents the gain error, and sin(φ) of the second term of Equation 2 and of the third term of Equation 3 represents an error caused by interference.
As described above, in case of the QAM, the phase error of the restored carrier has an effect on not only the gain error but also the error due to the interference, and thus this causes its effect to become more serious.
Accordingly, two conventional method of restoring the carrier in the receiving end have been proposed to solve the above-described problem.
One of them is a method of extracting a pilot signal from the frequency of a received signal, and synchronizing an output frequency and phase of a local oscillator with those of the received signal in the receiving end. This method is used for restoring the carrier of a vestigial side band (VSB) that is the ground wave of the conventional HDTV transmission system.
The other is a method of estimating the frequency and phase of the carrier directly from a suppression-modulated signal. This method has been widely used for the carrier restoration of the QAM and PSK of the conventional HDTV cable transmission system.
As the conventional carrier restoration method for estimating the frequency and phase of the carrier directly from the suppression-modulated signal, there have been proposed a square loop method as shown in FIG. 2, Costas loop method in FIG. 3, and decision feedback loop method in FIG. 4.
First, the square loop as shown in FIG. 2 restores the carrier of a transmitted signal S(t) by modulating the signal by a double side band/suppressed carrier (DSB/SC) phase amplitude modulation (PAM) as expressed by the following equation 4.S(t)=A(t)*cos(2πfct+φ)  [Equation 4]
In Equation 4, if the base-band signal level is symmetrical centering around 0, the average expected value becomes 0 as shown in the following equation 5.E[S(t)]=E[A(t)]=0  [Equation 5]
Accordingly, any phase information cannot be obtained from the average value of the received signal. At this time, the square loop as shown in FIG. 2 may be used as a method of driving a phase locked loop (PLL) by extracting the frequency component from 2πfct.
Specifically, the output S2(t) of a square section 21 is obtained by the following equation 6, and the average expected value is 0, the frequency component can be extracted from 2πfct.                                                                                                     ⁢                                                                    S                    2                                    ⁡                                      (                    t                    )                                                  =                                ⁢                                                                            A                      2                                        ⁡                                          (                      t                      )                                                        *                                                            cos                      2                                        ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                +                        ϕ                                            )                                                                                                                                              =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                                            A                      2                                        ⁡                                          (                      t                      )                                                                      +                                                      (                                          1                      /                      2                                        )                                    *                                                            A                      2                                        ⁡                                          (                      t                      )                                                        *                                      cos                    ⁡                                          (                                                                        4                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                +                                                  2                          ⁢                          ϕ                                                                    )                                                                                                                              [                  Equation          ⁢                                          ⁢          6                ]            
Accordingly, if the output S2(t) of the square section 21 passes through a band pass filter 22 having a center frequency of 2πfc, the DC component is removed, and only a component having a frequency of 2fc, phase of 2φ, and amplitude of ½*A2(t)*H(2fc) remains. Here, H(2fc) is the gain of the band pass filter.
In order to synchronize the oscillated frequency of a local oscillator 25 with the output of a band pass filter 22, a PLL process is performed. Specifically, the output of the band pass filter 22 and the output of the local oscillator 25 are multiplied through a multiplier 23, and the multiplied output is inputted to a loop filter 24. The output of the loop filter 24 is inputted to the local oscillator 25 again. That is, the loop filter 24 filters and accumulates the output of the multiplier 23 to detect a phase error, and output the phase error to the local oscillator 25. The local oscillator 25 generates a frequency sin(4πfct+2φ) that is in proportion to the phase error, and outputs the generated frequency to the multiplier 23 and a frequency divider 26.
The frequency divider 26 divides the output of the local oscillator 25 to obtain a restored carrier of sin(4πfct+2φ). Here, θ is an estimated value of φ, and the PLL is formed so as to effect φ−θ=0.
However, the carrier restoration by the above-described square loop has a phase ambiguity of 180° with respect to the phase of the received signal since the local oscillator 25 is synchronized with the frequency component of 2fc, and the restored carrier is generated through the frequency divider 26. This problem can be solved in a manner that the transmitting end performs a differential encoding, and the receiving end performs a differential decoding, but the frequency ambiguity still increases. Specifically, in case that the modulated signal contains information with M phases (i.e., the transmitted signal is given by the following equation 7), the frequency ambiguity increases to 2π/M if an M-involution element is used in replace of the square element and the frequency divider performs % M.S(t)=A(t)*cos[2πfct+φ+(2π/M)*(m−1)]  [Equation 7]
where, m=1, 2, 3, . . . M.
Next, the Costas loop method will be explained.
The Costas loop as shown in FIG. 3 restores the carrier of the transmitted signal expressed by Equation 4.
In FIG. 3, outputs Yc(t) and Ys(t) of first and second multipliers 31 and 32 can be expressed by the following equations 8 and 9.                                                                                           Y                  c                                ⁡                                  (                  t                  )                                            =                            ⁢                                                [                                                            S                      ⁡                                              (                        t                        )                                                              +                                          N                      ⁡                                              (                        t                        )                                                                              ]                                *                                  cos                  ⁡                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          c                                                ⁢                        t                                            +                      θ                                        )                                                                                                                          =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                      [                                                                  A                        ⁡                                                  (                          t                          )                                                                    +                                                                        N                          c                                                ⁡                                                  (                          t                          )                                                                                      ]                                    *                  cos                  ⁢                                                                          ⁢                  Δϕ                                +                                                                                                      ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                                            N                      s                                        ⁡                                          (                      t                      )                                                        *                  sin                  ⁢                                                                          ⁢                  Δϕ                                +                                  2                  ⁢                                      f                    c                                                                                                          [                  Equation          ⁢                                          ⁢          8                ]                                                                                                                ⁢                                                                    Y                    c                                    ⁡                                      (                    t                    )                                                  =                                ⁢                                                      [                                                                  S                        ⁡                                                  (                          t                          )                                                                    +                                              N                        ⁡                                                  (                          t                          )                                                                                      ]                                    *                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                +                        θ                                            )                                                                                                                                              =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                      [                                                                  A                        ⁡                                                  (                          t                          )                                                                    +                                                                        N                          c                                                ⁡                                                  (                          t                          )                                                                                      ]                                    *                  sin                  ⁢                                                                          ⁢                  Δϕ                                +                                                                                                      ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                                            N                      s                                        ⁡                                          (                      t                      )                                                        *                  cos                  ⁢                                                                          ⁢                  Δϕ                                +                                  2                  ⁢                                      f                    c                                                                                                          [                  Equation          ⁢                                          ⁢          9                ]            
Here, the components of Δφ=φ−θ, and 2fc are removed passing through first and second base-band pass filters 32 and 36. The outputs of the first and second base-band pass filters 32 and 36 are multiplied by a multiplier 33 to produce an error signal as expressed by the following equation 10.                                                                         e                ⁡                                  (                  t                  )                                            =                            ⁢                                                                    (                                          1                      /                      8                                        )                                    *                                      {                                                                                            [                                                                                    A                              ⁡                                                              (                                t                                )                                                                                      +                                                                                          N                                c                                                            ⁡                                                              (                                t                                )                                                                                                              ]                                                2                                            -                                                                        N                          s                          2                                                ⁡                                                  (                          t                          )                                                                                      }                                    *                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  ϕ                                -                                                                                                      ⁢                                                (                                      1                    /                    4                                    )                                *                                                      N                    s                                    ⁡                                      (                    t                    )                                                  *                                  [                                                            A                      ⁡                                              (                        t                        )                                                              +                                                                  N                        c                                            ⁡                                              (                        t                        )                                                                              ]                                *                cos                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                ϕ                                                                        [Equation  10]            
In Equation 10, it can be recognized that the error signal e(t) is composed of a desired signal component of A2(t)*sin 2Δφ, component of signal*noise, and component of noise*noise. Here, a matched filter may be suitably used as the first and second base-band pass filters 32 and 36. If the matched filter is used, the noise mixed to the loop can be reduced.
The operation of a loop filter 37 that received the output of the multiplier 33 and the operation of a local oscillator 28 are the same as those in the above-described square loop method, and the detailed explanation thereof will be omitted. That is, the Costas loop method is equivalent to the square loop method, and has the phase ambiguity of 180°.
Next, the decision feedback loop method will be explained.
The above-described Costas loop method has the problem in that as the error signal is multiplied by the noise, the noise is amplified to its square value. This problem can be solved by adding a decision element to one side of the Costas loop as shown in FIG. 3. This type of carrier restoration is called the decision feedback loop method, which is illustrated in FIG. 4. Referring to FIG. 4, a sampler 43 and a decision element 45 are arranged between a first base-band pass filter 42 and a multiplier 49 of the carrier restoration apparatus of FIG. 3. Here, the sampler 43 receives from a timing restoration section 44 timing errors of present symbols produced through the base-band signal process, and performs an interpolation to reduce the errors among the output signals of the first base-band pass filter 42. Also, the decision element 45 generates and outputs to the multiplier 49 decision signals matching respective signal levels of the base-band signals outputted from the sampler 43.
If there is no error in the decision element in FIG. 4, the output of the decision element 45 will be the base-band signal A(t) from which the noise is removed. Accordingly, if the phase error signal e(t) is developed, the square component of the noise is vanished as shown in the following equation 1.                                                                         e                ⁡                                  (                  t                  )                                            =                            ⁢                                                (                                      1                    /                    2                                    )                                *                                  A                  ⁡                                      (                    t                    )                                                  *                                  {                                                                                    [                                                                              A                            ⁡                                                          (                              t                              )                                                                                +                                                                                    N                              c                                                        ⁡                                                          (                              t                              )                                                                                                      ]                                            *                      sin                      ⁢                                                                                          ⁢                      Δ                      ⁢                                                                                          ⁢                      ϕ                                        -                                                                                                                                                          ⁢                                                                            N                      s                                        ⁡                                          (                      t                      )                                                        *                  cos                  ⁢                                                                          ⁢                  Δϕ                                }                            +                              2                ⁢                                  f                  c                                                                                                        =                            ⁢                                                                    (                                          1                      /                      2                                        )                                    *                                                            A                      2                                        ⁡                                          (                      t                      )                                                        *                  sin                  ⁢                                                                          ⁢                  Δϕ                                +                                                      (                                          1                      /                      2                                        )                                    *                                                                                                                      ⁢                                                                    A                    ⁡                                          (                      t                      )                                                        *                                      [                                                                                                                        N                            c                                                    ⁡                                                      (                            t                            )                                                                          *                        sin                        ⁢                                                                                                  ⁢                        Δϕ                                            -                                                                                                    N                            s                                                    ⁡                                                      (                            t                            )                                                                          *                        cos                        ⁢                                                                                                  ⁢                        Δϕ                                                              ]                                                  +                                  2                  ⁢                                      f                    c                                                                                                          [Equation  11]            
However, the decision feedback loop method as described above also has the following problems.
First, since an elaborate high-quality tuner should be used according to a small acquisition/tracking range, the cost for preparing the tuner is increased. That is, a tuner with a small frequency offset and small phase jitter during the carrier restoration has a good performance, and such a tuner having the good performance is typically expensive.
Second, the BER performance of the receiver is lowered due to a large residual phase jitter.
Third, the acquisition/tracking performance with respect to a small input SNR deteriorates. That is because if the receiving power (i.e., SNR) of the input signal is small, the error detection section of the conventional carrier restoration section produces an inaccurate error.
Fourth, the acquisition/tracking performance with respect to the ISI/ghost channel deteriorates widely. Even in the channel having a strong ISI/ghost, the error detection section also produces an inaccurate error in the same manner.